Series and Parallel Resistors

1. Practice on Generating and Measuring Current, Voltage, and Resistance

1. Obtain a current source, a voltage source, and two multimeters that can measure voltage, current, and resistance.
2. Obtain two 100-Ω resistors and two 10-Ω resistors.
3. Obtain a breadboard, which is a convenient platform to connect and organize different circuit elements. The breadboard has many groups of pins. The pins of each group are connected together at the back of the board, and wires plugged into the same group are shorted together. A wire plugged into the same group of pins as a terminal of a circuit element is connected to that terminal. Different terminals of a circuit element not meant to be shorted should be plugged into different pin groups. In the following, the action of connecting two terminals means plugging them into the same pin group (in the figures, distinctive nodes labelled "a", "b", and "c" represent distinctive pin groups on the breadboard). This is done provided that such terminals are made of wires that can be conveniently inserted into a pin hole. Otherwise, it is possible to use cables, banana plugs, and clamps to make electrical connections (for example, from a terminal on the instrument to an exposed pin leg on the breadboard).
4. Connect the output terminal of the current source to one terminal of the 100-Ω resistor, and then connect the other terminal of the resistor back to the other terminal of the current source.
5. Generate 1 mA current through the resistor.
6. Select the voltage measurement or voltmeter mode of the multimeter, and connect the two terminals of the multimeter to the two terminals of the resistor. Measure the voltage drop cross the resistor.
7. A positive reading means that the potential at the positive terminal of the multimeter is higher than that at the negative terminal. Use the voltage reading to verify the Ohm's law relationship (Figure 3).
8. Next, connect one terminal of a voltage source to one terminal of the resistor, and connect the other terminal of the resistor back to the other terminal of the voltage source. Produce a 10 V voltage across the 100-Ω resistor.
9. Use the multimeter in the current measurement or ammeter mode, and connect the probes in series with the resistor. Measure the current through the resistor.
   1. A positive reading means that the electrical current is flowing from the positive terminal of the multimeter to the negative terminal. Then, verify Ohm's law (Figure 4).
   2. Note that the multimeter needs to be in series with a resistor to measure its current (ammeter), but needs to be in parallel with a resistor to measure its voltage drop (voltmeter). In these measurements, assume that the "internal" resistance of the ammeter is very small but that of the voltmeter is very large. If this is not rigorously true then the current or voltage measured by the meter would be different from the value before the connection of the meter.
10. Finally, directly measure the resistance using the multimeter (Figure 5) by selecting the resistance measurement mode. Connect the two terminals of the meter with the two terminals of the resistor and read the resistance. Confirm that the resistance makes sense based on the previous current and voltage measurements.

Figure 3: Circuit diagram of sourcing a current through resistor R and measuring voltage.

Figure 4: Circuit diagram of sourcing a voltage across resistor R and measuring current.

Figure 5: Connection of a multimeter to measure resistance of a resistor.

2. Resistors in Series

1. Connect two 100-Ω resistors in series (refer to Figure 1). On the breadboard, this means plugging the two ends of the first resistor into two different pin groups (not shorted), say group a and b, and plugging the two ends of the second resistor into pin groups b and c (c is yet another pin group not shorted to a and b).
   1. Connect a common current of 10 mA through both resistors using a current source as described in step 1.4.
   2. Using a multimeter in voltmeter mode, measure the voltage drop across each resistor. Then confirm the resistance values of R₁ and R₂ using Ohm's law.
   3. Now use the voltmeter to measure the voltage V across the entire series combination (between points a and c in Figure 1), and obtain the total series resistance.
   4. Enter the measured resistance values, as shown in Table 1.
   5. Disconnect the power sources and meters, then use a voltage source to provide a total of 10 V across both resistors (between points a and c).
   6. Use a multimeter in ammeter mode to measure the current (I₁) entering R₁, and the current (I₂) entering R₂.
   7. Verify that I₁ is equal to I₂ (or approximately equal; any small difference might be due to slightly different configurations, including wire resistances that changed slightly).
2. Repeat the procedure in step 2.1 for two 10-Ω resistors in series, and measure the wire resistance using the multimeter.
3. Repeat the procedure in step 2.1 for one 100-Ω resistor in series with one 10-Ω resistor, and repeat the resistance measurements.

3. Resistors in Parallel

1. Connect two 100-Ω resistors in parallel (refer to Figure 2). On the breadboard, plug the two ends of each resistor into two pin groups, say a and b.
   1. Source a common voltage drop of V = 10 V using a voltage source.
   2. Use a multimeter to measure the current I₁ entering R₁, thus confirming that R₁ = V/I₁. Then, measure I₂ entering R₂, thus confirming that R₂ = V/I₂.
   3. Now put the amp meter in front of the parallel combination (before point a in Figure 2), and obtain the total series resistance R = V/I.
2. Repeat the above in step 3.1 for two 10-Ω resistors in parallel, and again for one 100-Ω resistor in parallel with one 10-Ω resistor.

4. LEDs in Series and Parallel Connection

1. Obtain two small LED light sources, which can be treated as two resistors.
2. Connect 1 V source to power 1 LED (similar connection as step 1.5), and observe its brightness.
3. Now connect the two LEDs in parallel between the 1 V source (similar connection as in step 3.1), and observe their brightness.
4. Now connect the two LEDs in series and between the 1 V source (similar connection as step 2.1.5), and observe their brightness again.